# Normal Subgroups of a Group

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Modern Algebra

Group Theory (XLIV)

Subgroups of a Group

Normal Subgroups of a Group

Subgroups of a Group Normal Subgroups of a Group Suppose H is the only subgroup of order O(H) in the finite group G. Prove that H is a normal subgroup of G.

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#### Solution Summary

This solution is comprised of a detailed explanation to prove that H is a normal subgroup of G

where H is the only subgroup of order O(H) in the finite group G. The solution is detailed and well presented.

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